The Ultraviolet Behavior Of Quantum Gravity

TL;DR

This paper explores a novel quantum gravity theory using fakeons to address ultraviolet divergences, demonstrating how renormalizability and unitarity can coexist through one-loop calculations and the disentanglement of self-energy parts.

Contribution

It introduces a new quantization approach with fakeons in higher-derivative gravity, showing how it maintains unitarity and renormalizability at the quantum level.

Findings

Fakeons turn poles into fake degrees of freedom.

Renormalizability is compatible with unitarity via fakeons.

Absorptive part relates to matter field central charge.

Abstract

A theory of quantum gravity has been recently proposed by means of a novel quantization prescription, which is able to turn the poles of the free propagators that are due to the higher derivatives into fakeons. The classical Lagrangian contains the cosmological term, the Hilbert term, $\sqrt{-g}R_{\mu \nu }R^{\mu \nu }$ and $\sqrt{-g}R^{2}$. In this paper, we compute the one-loop renormalization of the theory and the absorptive part of the graviton self energy. The results illustrate the mechanism that makes renormalizability compatible with unitarity. The fakeons disentangle the real part of the self energy from the imaginary part. The former obeys a renormalizable power counting, while the latter obeys the nonrenormalizable power counting of the low energy expansion and is consistent with unitarity in the limit of vanishing cosmological constant. The value of the absorptive part is related to the central charge $c$ of the matter fields coupled to gravity.